7. Is the following a function? {(1,3), (2,4), (3,5),(4,10), (5,15),(3,5)}

Yes it's a function.

Explanation:

While x = 3 does repeat itself, the y value repeats itself as well for this particular x value. In other words, we have two copies of (3,5). Toss out any duplicate (x,y) pairings and we have this simplified set:

{(1,3), (2,4), (3,5), (4,10), (5,15)}

At this point, we don't have any repeated x values. Therefore, we have a function. Any input x leads to exactly one y output. The y values are allowed to repeat themselves.

Extra info:

The domain is {1,2,3,4,5} which is the set of x coordinatesThe range is {3,4,5,10,15} which is the set of y coordinates.This function is one-to-one because there are no repeat y values.

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

If jon had $4.00 then takes away $2.25, then he should have $1.75 left. $4.00 - $2.25 = $1.75 hope this ; )